177 
1918-19.] The Propagation of Earthquake Waves. 
ray which coincides with the epicentral radius are also estimated and 
entered. 
In fig. 6 the successive positions of the wave-front for the Primary 
waves are indicated by full lines cutting the rays orthogonally. The very 
similar curves drawn in broken line are the successive positions of the 
wave-front for the Secondary waves. They would intersect orthogonally 
the Secondary rays if these were drawn in. 
As already stated, the Primary and Secondary waves were transmitted 
along paths which are of much the same general character. How com- 
paratively slight the differences are may be indicated by a comparison of 
the two wave moduli on which the speeds of propagation of the two types 
of wave are believed to depend. For an elastic medium of density p, 
rigidity n, and incompressibility k, the speeds of propagation of the two 
waves are given by the formulae 
Knowing the values of the two velocities for various values of the 
distance from the earth’s centre, we may calculate the ratio k/n and also 
Poisson’s ratio of transverse contraction to longitudinal elongation under 
the influence of a longitudinal pull. 
These are given in the following table : — 
r. 
R. 
v/u. 
k/n. 
Poisson's 
ratio. 
1 
6738 
1-80 
1-92 
•272 
•89 
6000 
1-80 
1*89 
•275 
•816 
5500 
1-79 
1-87 
•273 
•742 
5000 
1-81 
1*93 
•280 
•668 
4500 
1-87 
2*16 
•3 
•594 
4000 
1-88 
2-19 
•302 
•445 
3000 
1-87 
2*15 
•298 
For distances from the earth’s centre greater than three-fourths of the 
radius the two elastic constants seem to vary according to the same law. 
so that the ratio of the velocities remains at the value T8 throughout. 
For distances less than this, however, the ratio increases to nearly 1*9, and 
this increase takes place fairly suddenly. Either the incompressibility has 
increased relatively to the rigidity, or the rigidity has diminished relatively 
to the compressibility. Now the curves showing the velocities in terms of 
the distances from the centre indicate that the Secondary wave velocity 
becomes constant at positions somewhat nearer the surface than where the 
VOL. xxxix. 12 
